Robotics: Trajectory Planning Basics

Terminology

• A path shows the points the manipulator goes through to do what it needs to.
• Path can be determined in joint space or Cartesian space.
• A trajectory is the path with a time law, specifying velocities and accelerations.
• Trajectory can also be specified in joint or Cartesian space.
• Via points (knot points) are intermediate locations between the start/end points that the manipulator passes through

Trajectory Planning

• Trajectory planning involves using polynomial functions to "interpolate" or "approximate" the desired path.
• This method creates a series of time-based "control set points" for controlling the manipulator.

Joint Space vs. Cartesian Space Trajectory Planning

• Joint space trajectory planning specifies each point as the desired position/orientation of the end-effector frame, relative to the base frame
• Inverse kinematics converts these points into desired joint variables.
• It finds a smooth function for each joint that passes through these points.
• Cartesian space trajectory planning explicitly defines the path in Cartesian space.
• Path constraints are given in Cartesian coordinates, but joint actuators move in joint coordinates to achieve the desired trajectory.

Trajectory Generation

• Trajectory generation creates inputs for the motion control system.
• These inputs make sure the planned trajectory happens correctly.

Path Profile

• Initial position is required for trajectory planning
• There are 14 boundary conditions for planning
• Velocity is also required for trajectory planning
• Acceleration is also needed for trajectory planning

Requirements of Planning

• Initial planning requires position to be given
• Initial planning requires Velocity to be given or normally zero
• Initial planning requires Acceleration to be given or normally zero
• Final postion is required for planning
• Velocity is required given or normally zero
• Acceleration is required given or normally zero

Intermediate Position

• Set-down position is given or continuous with previous trajectory segment), as well as velocity and acceleration
• Lift-off position is given or continuous with previous trajectory segment, velocity and acceleration

Steps to planning

• A task description must be given: point by point, or continious path
• A trajectory planning must be used which is either joint space, or cartesian space
• The trajectory must be computed with time values in real time.

Learn about robotic trajectory planning: paths, trajectories, and the distinction between joint space and Cartesian space approaches. Understand how polynomial functions are used to create time-based control set points for manipulators, ensuring smooth and efficient motion.